The bandwidth of a filter can be described by its quality factor (Q) and its center frequency .omega..sub.0. Q is a measure of the sharpness of the peak of the bandwidth response function. For a simple resonant circuit, such as an LC filter, Q can be interpreted as the ratio of .omega..sub.0 to the full width of the peak between the upper and lower half power points (3 dB). Another measure of the filter performance is the noise figure, which is the signal to noise ratio of the applied input to the signal to noise ratio at the output. It is desirable that the noise figure be low to preserve dynamic range.
Generally, LC filters having inductors and capacitors are used where variable frequency selectivity is required. In conventional variable, wideband bandpass filters, the bandwidth of the filter can be altered as desired by adjusting a variable resistor. FIG. 1 illustrates a prior art simplified circuit topology, where the bandwidth of the filter is adjusted by varying the resistance. Such a filter is used, for example, in the Hewlett-Packard Company HP 8552B spectrum analyzer. The Q and .omega..sub.0 of the circuit are ##EQU1## If the JFET shown in FIG. 1 is assumed to have infinite input impedance then the bandwidth is limited in the widest mode by the 50 .OMEGA. input and in the narrowest mode by the maximum resistance of the variable resistor.
There are a few problems with this filter. In narrow bandwidths, the large resistance of R causes the noise figure to be degraded. Using an active device, such as a JFET, adds parasitic capacitance to the tank. Thirdly, the input impedance of the filter does not match the 50 .OMEGA. input.
Another simplified circuit topology of a prior art filter, used in the Hewlett-Packard Company HP 8566B spectrum analyzer, is illustrated in FIG. 2. This circuit has good input and output impedance matches but still has a poor noise figure. In addition, because the tank is connected to the collector of Q1, the filter has bad distortion due to the high RF voltage present on the tank.
Each of the aforementioned filters uses active devices to provide a variable bandwidth filter, which introduces distortion into the filter. Furthermore, the resulting circuits are DC power intensive, particularly with pin diodes or bipolar transistors as the active devices.
What is desirable is a variable bandwidth filter using passive elements which do not introduce distortion. It would also be beneficial if the filter was DC power efficient.